Direct and Inverse Variation
Joint Variation
Solving Square Root Functions
Converting between rational and radical
Word Probems!
100

Does the equation x = 5y model direct variation, inverse variation, or neither?

Direct!
100

If y varies jointly as x and z, and y = 12 when x = 9 and z = 3, find z when y = 6 and x = 15.

z = 9/10
100
sqrt(x) = 4
x = 16
100

Convert between rational and radical form: 


51/4

fourth root of 51

100

The cost of producing pencils varies directly with the number of pencils produced. If the cost of producing 6,000 pencils is $400, then what will be the cost of production for 10,000 pencils?

$600
200

Find y when x =1.5, if y varies directly as x and y =- 16 when x=6.

y = -4
200

If y varies jointly as x and z, and y = 33 when x = 9 and z = 12, find y when x = 16 and z = 22.

y = 968/9
200
sqrt(r+9) = 1
r = -8
200

Convert between rational and radical form: 

sqrt(3x)3

3x 3/2

200

6 people can do a job in 10 hours. How long will it take 9 people to do the same job?

6 hours and 40 min
300

If y varies inversely with x and y = 0.3 when x = 3.5, then find the value of y when x = 3.

y = .35
300

Suppose y varies jointly with x and z. If y = 20 when x =2 and z = 5, find y when x =14 and z=8.

y = 224
300
3sqrt(25k) = 15
k = 1
300

Convert between rational and radical form: 

(2m2) 1/3

cube root 2m2

300

A pump empties a swimming pool in 40 minutes at the rate of 1400 L/min. If the rate of pumping is 2000 L/min, how long does it take to empty the swimming pool?

28 minutes
400

 If y varies inversely as x and x=7 when y =21, find y when x =42.

y = 3.5 
400

 If p varies jointly as q and r squared, and p = 225 when q = 4 and r = 3, find p when q = 6 and r = 8.

p = 2400
400
sqrt(19x -2) -1 = 5
x = 2
400

Convert between rational and radical form: 

6x-4/2

1 / sqrt(6x4)

400

 According to Hooke's Law, the force needed to stretch a spring is proportional to the length of the spring stretched. If 41 pounds stretches a spring 3 inches, how much will the spring be stretched by a force of 58 pounds?

4.24 inches 
500
Y varies directly as the cube of x. If y = 1,000 when x=2, find y when x =3. 
y = 3,375
500

If a varies jointly as b cubed and c, and a = 36 when b = 4 and c = 6, find a when b = 2 and c = 14.

a = 21/2
500

3 = (2n -2)1/2 + 1

n = 3
500

Convert between rational and radical form: 

(5x-6)1/3

1 / 5x2

500

The volume of a can varies jointly as the height of the can and the square of its radius. A can with an 8 inch height and 4 inch radius has a volume of 402.12 in3. What is the volume of a can that has a 2 inch radius and a 10 inch height? 

125.66 in3

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